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Classe « Generator »

Méthode numpy.random.Generator.multinomial

Signature de la méthode multinomial

def multinomial(self, n, pvals, size=None) 

Description

help(Generator.multinomial)

        multinomial(n, pvals, size=None)

        Draw samples from a multinomial distribution.

        The multinomial distribution is a multivariate generalization of the
        binomial distribution.  Take an experiment with one of ``p``
        possible outcomes.  An example of such an experiment is throwing a dice,
        where the outcome can be 1 through 6.  Each sample drawn from the
        distribution represents `n` such experiments.  Its values,
        ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the
        outcome was ``i``.

        Parameters
        ----------
        n : int or array-like of ints
            Number of experiments.
        pvals : array-like of floats
            Probabilities of each of the ``p`` different outcomes with shape
            ``(k0, k1, ..., kn, p)``. Each element ``pvals[i,j,...,:]`` must
            sum to 1 (however, the last element is always assumed to account
            for the remaining probability, as long as
            ``sum(pvals[..., :-1], axis=-1) <= 1.0``. Must have at least 1
            dimension where pvals.shape[-1] > 0.
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn each with ``p`` elements. Default
            is None where the output size is determined by the broadcast shape
            of ``n`` and all by the final dimension of ``pvals``, which is
            denoted as ``b=(b0, b1, ..., bq)``. If size is not None, then it
            must be compatible with the broadcast shape ``b``. Specifically,
            size must have ``q`` or more elements and size[-(q-j):] must equal
            ``bj``.

        Returns
        -------
        out : ndarray
            The drawn samples, of shape size, if provided. When size is
            provided, the output shape is size + (p,)  If not specified,
            the shape is determined by the broadcast shape of ``n`` and
            ``pvals``, ``(b0, b1, ..., bq)`` augmented with the dimension of
            the multinomial, ``p``, so that that output shape is
            ``(b0, b1, ..., bq, p)``.

            Each entry ``out[i,j,...,:]`` is a ``p``-dimensional value drawn
            from the distribution.

        Examples
        --------
        Throw a dice 20 times:

        >>> rng = np.random.default_rng()
        >>> rng.multinomial(20, [1/6.]*6, size=1)
        array([[4, 1, 7, 5, 2, 1]])  # random

        It landed 4 times on 1, once on 2, etc.

        Now, throw the dice 20 times, and 20 times again:

        >>> rng.multinomial(20, [1/6.]*6, size=2)
        array([[3, 4, 3, 3, 4, 3],
               [2, 4, 3, 4, 0, 7]])  # random

        For the first run, we threw 3 times 1, 4 times 2, etc.  For the second,
        we threw 2 times 1, 4 times 2, etc.

        Now, do one experiment throwing the dice 10 time, and 10 times again,
        and another throwing the dice 20 times, and 20 times again:

        >>> rng.multinomial([[10], [20]], [1/6.]*6, size=(2, 2))
        array([[[2, 4, 0, 1, 2, 1],
                [1, 3, 0, 3, 1, 2]],
               [[1, 4, 4, 4, 4, 3],
                [3, 3, 2, 5, 5, 2]]])  # random

        The first array shows the outcomes of throwing the dice 10 times, and
        the second shows the outcomes from throwing the dice 20 times.

        A loaded die is more likely to land on number 6:

        >>> rng.multinomial(100, [1/7.]*5 + [2/7.])
        array([11, 16, 14, 17, 16, 26])  # random

        Simulate 10 throws of a 4-sided die and 20 throws of a 6-sided die

        >>> rng.multinomial([10, 20],[[1/4]*4 + [0]*2, [1/6]*6])
        array([[2, 1, 4, 3, 0, 0],
               [3, 3, 3, 6, 1, 4]], dtype=int64)  # random

        Generate categorical random variates from two categories where the
        first has 3 outcomes and the second has 2.

        >>> rng.multinomial(1, [[.1, .5, .4 ], [.3, .7, .0]])
        array([[0, 0, 1],
               [0, 1, 0]], dtype=int64)  # random

        ``argmax(axis=-1)`` is then used to return the categories.

        >>> pvals = [[.1, .5, .4 ], [.3, .7, .0]]
        >>> rvs = rng.multinomial(1, pvals, size=(4,2))
        >>> rvs.argmax(axis=-1)
        array([[0, 1],
               [2, 0],
               [2, 1],
               [2, 0]], dtype=int64)  # random

        The same output dimension can be produced using broadcasting.

        >>> rvs = rng.multinomial([[1]] * 4, pvals)
        >>> rvs.argmax(axis=-1)
        array([[0, 1],
               [2, 0],
               [2, 1],
               [2, 0]], dtype=int64)  # random

        The probability inputs should be normalized. As an implementation
        detail, the value of the last entry is ignored and assumed to take
        up any leftover probability mass, but this should not be relied on.
        A biased coin which has twice as much weight on one side as on the
        other should be sampled like so:

        >>> rng.multinomial(100, [1.0 / 3, 2.0 / 3])  # RIGHT
        array([38, 62])  # random

        not like:

        >>> rng.multinomial(100, [1.0, 2.0])  # WRONG
        Traceback (most recent call last):
        ValueError: pvals < 0, pvals > 1 or pvals contains NaNs

        

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